Hamilton-Wenham Regional School District
HWRHS Common Core Standards Algebra 2
Algebra 2 Units
Unit 1: Functions (Ch. 1 and 2)
Unit 2: Quadratics (Ch. 5)
Unit 3: Polynomials (Ch. 6)
Unit 4: Powers, Roots, Radicals (Ch. 7)
Unit 5: Exponential and Logarithmic Functions (Ch. 8)
Unit 6: Rational Equations and Functions (Ch. 9)
Unit 7: Trigonometric Functions (Ch. 13 and 14)
Unit 8: Statistics and Probability (Ch. 12)
Algebra 2 Overview
Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to
include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions,
and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic
equations over the set of complex numbers and solving exponential equations using the properties of logarithms.
The Mathematical Practice Standards apply throughout each unit and together with the content standards, prescribe that
students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense
of problem situations. Algebra 2 by Larson, Boswell, Kanold, and Stiff (McDougal Littell, 2004) is used as the primary
resource. Chapter and content numbers included in parentheses refer this textbook.
Algebra 2 Prerequisites
Algebra 2 students have successfully completed Algebra 1 and Geometry.
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
First Quarter
Conceptual Category
Functions
Unit 1(Ch. 1 and 2)
Unit 1.1 (1.4):
Rewriting
Equations and
Formulas
A-CED 4
Unit 1.2 (1.5):
Problem Solving
Using Algebraic
Models
A-CED 1, 2, 3
Unit 1.3 (2.7):
Piecewise
Functions
A-REI 11
F-IF 7b
Unit 1.4: (2.8):
Absolute Value
A-REI 11
F-IF 7b
F-BF 3
Functions
10 days
Mathematical Practices
and Essential Questions
Prior Learning
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)
(IA): Rewrite various formulas for specific variable
(IA): pg. 29 #12-30
SMP : 2, 5
Working with
multivariable
equations
SMP: 1, 2, 4, 5
How do you solve real
world problems using
graphs and equations?
Solving linear
equations
(IA): Model solving linear word problems
(IA): Individual or group work: practice solving linear
word problems
(IA): pg. 38 #16-24
SMP: 4,5,6
What is a piecewise
function?
What is a step
function?
How can these
functions be applied?
SMP: 4, 5, 6
What does an absolute
value graph look like?
Why?
Graphing linear
equations and
inequalities
(IA): Review graphing basic linear equations
(IA): Use examples to demonstrate how to graph
step and piecewise functions
(IA): pg. 117 #14-28, 36- 39
(FA): Quiz: 1.4, 1.5, 2.7
Solving absolute
value equations
Understand the
concept of
absolute value
(IA): Use examples to demonstrate how to graph an
absolute value function
(IA): Introduce the effects of h and k
(transformations) on an absolute value graph
(IA): pg. 125 #14-24, 34-38
(SA): Test Unit 1
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
First Quarter
Conceptual Category
Functions
Unit 2 Quadratics (Ch. 5)
21 days
CC Standard and
Content
Mathematical Practices Prior Learning
and Essential Questions
Unit 2.1 (5.1):
Graphing Quadratic
Functions
A-CED 2
A-REI 11
F-IF 4, 5
F-IF 7b
F-BF3
Unit 2.2 (5.2):
Solving Quadratic
Equations by
Factoring
A-CED 1
A-SSE 1, 2
F-IF 4
SMP: 4, 5, 6
How do we use our
understanding of
quadratics to graph a
quadratic function?
Solving and
graphing basic
quadratic
equations and
functions
SMP: 1, 2, 7, 8
How can we find the
solutions (x-intercepts)
of a quadratic
equation?
Factoring basic
quadratic
equations.
Unit 2.3 (5.3):
Solving Quadratic
Equations by
Finding Square
Roots.
A-CED 1
Unit 2.4 (5.4):
Complex Numbers
N-CN 1, 2, 7, 8
SMP: 1, 5, 7 ,8
How can we find the
solutions (x-intercepts)
of a quadratic
equation?
Understanding
and using square
roots.
Unit 2.5(5.6):
Quadratic Formula
and the
Discriminant
A-CED 1
N-CN 7
SMP: 1, 4, 6
How can we find the
solutions (x-intercepts)
of a quadratic
equation?
What does finding a
zero mean?
SMP: 1, 2, 5
What is an imaginary
number?
Why do we have
imaginary numbers?
Solving basic
quadratic
equations
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)
(IA): Review basic quadratic graph
(IA): Show how to find vertex, axis of symmetry,
and basic characteristics of the graph
(IA): Introduce standard, vertex and intercept forms
(IA): Writing equations in standard form
(IA): pg. 253 #17-49
(FA): Quiz Graphing
(IA): Review factoring methods
(IA): Introduce special factoring methods
(difference of perfect squares, perfect square
trinomials)
(IA): Review solving quadratic equations by
factoring
(IA): Create a quadratic equation to solve a word
problem
(IA) pg. 260 #23-88
(FA): Quiz Factoring
(IA): Simplify a radical expression
(IA): Solve equations by finding square roots
(IA): Understand which method (square roots or
factoring) to utilize to solve an equation.
(IA) pg. 267 #19-68
(IA): Introduce the complex number i
(IA): Perform basic operations with complex
numbers
(IA): Solving quadratic equations involving complex
number solutions
(IA): pg. 277 #17-55
(IA): Introduce the quadratic formula
(IA): Review simplifying radical expressions
(IA): Relate the solutions to a quadratic equation to
the graph of the quadratic
(IA): Create a quadratic to model real-world
problems and use the quadratic formula to solve
(IA): Understand which method (factoring, square
roots, quadratic formula) to use to solve an
equation
Unit 2.6 (5.8):
Modeling With
Quadratic
Functions
A-CED 1
F-BF 1
SMP: 1, 4, 6
What relationships can
be modeled by a
quadratic?
Scatter-Plots and
lines of best fit
(IA): pg. 295 #17-64
(FA): Quiz: Solving Quadratic Equations
(IA): Writing quadratic equations based on given
information using the different forms (standard,
intercept, vertex)
(IA): Use graphing calculator to plot a scatter plot
and find a line of best fit
(IA): pg. 309 #7-24, 36-39
(SA): Ch. 5 Test
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
Second Quarter
Conceptual Category
Algebra
Unit 3 Polynomials (Ch. 6) 22days
CC Standard and
Content
Mathematical Practices Prior Learning
and Essential Questions
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)
(IA): Review properties of exponents
(IA): pg. 326 #16-47
Unit 3.1 (6.1):
Properties of
Exponents
N-RN-1
SMP: 5, 7, 8
How do we use the
properties of
exponents?
Understanding
and use
properties of
exponents
Unit 3.2 (6.2):
Evaluating and
Graphing
Polynomial
Functions
A-REI 11
F-IF 4
F-IF 7c
SMP: 5, 6
How do you evaluate
and graph a polynomial
function?
Graphing linear
and quadratic
equations.
(IA): Review direct substitution
(IA): Introduce synthetic substitution
(IA): Introduce end behavior
(IA): Use the graphing calculator or application to
graph polynomials
(IA): pg. 333 # 27-46, 49-64
(SA): Quiz: Properties of Exponents and Evaluating
Functions
Unit 3.3 (6.3):
Adding,
Subtracting, and
Multiplying
Polynomials
A-APR 1
Unit 3.4 (6.4):
Factoring and
Solving Polynomial
Equations
A-CED 1
A-SSE 1, 2
SMP: 5, 8
Are polynomials closed
under the operations
of addition,
subtraction, and
multiplication
SMP: 1, 2, 5
Why do I want to factor
polynomials?
Adding,
Subtracting, and
Multiplying linear
expressions
(IA): Demonstrate how to add, subtract, and
multiply polynomials using examples in the book
(IA): pg. 341 # 13-61
Factoring
quadratics
(IA): Review factoring of quadratics and solving
quadratics by factoring
(IA): Introduce factoring by grouping to factoring a
polynomial
(IA): Solve polynomials by factoring
(IA): pg. 349 #18-26, 41-85
F-IF 4
Unit 3.5 (6.5): The
Remainder and
Factor Theorems
A-APR 2, 3
SMP: 2, 4
How do I find the zeros
of a polynomial?
Long division
Factoring
quadratics
Unit 3.6 (6.6):
Finding Rational
Zeros
A-APR 2, 3
SMP: 2, 4, 7
How do I find the zeros
of a polynomial?
Factoring
quadratics
Unit 3.7 (6.7): Using SMP: 2, 4, 7
the Fundamental
How do I find the zeros
Theorem of Algebra of a polynomial?
N-CN 9
A-APR 3
Factoring
quadratics
Unit 3.8 (6.8):
Analyzing Graphs of
Polynomial
Functions
A-REI 11
F-IF 4, 5
F-IF 7c
SMP: 2,3, 5
What is end behavior?
What is the difference
between local or
absolute
minimum/maximum
and how do I find
them?
(IA): Review long division and apply it to dividing
polynomials
(IA): Review synthetic substitution and relate it to
synthetic division
(IA): Introduce and explain the Remainder Theorem
(IA): pg. 356 #16-54
(SA): Quiz: Solving Polynomials by factoring or
synthetic division
(IA): Review synthetic division
(IA):Use the synthetic division and Rational Zero
Theorem to find the rational zeros of a polynomial
(IA): pg. 362 #15-58
(IA): Introduce and explain the Fundamental
Theorem of Algebra
(IA): Find all zeros (real and imaginary) of a
polynomial
(IA): Use a graphing calculator or application to
approximate zeros
(IA): Apply theorems to solve real-world problems
(IA): pg. 369 #21-54
(IA): Review end behavior
(IA): Talk about turning points and how they relate
to the degree of the polynomial
(IA): Find the real zeros of a graph and relate to the
degree of the polynomial
(IA): Find all minimums and maximums (local or
absolute) and describe the difference
(IA): pg. 377 #23-34
(SA): Ch. 6 Test
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
Second Quarter
Conceptual Category
Functions
Unit 4 Powers, Roots, and Radicals (Ch. 7)
15 days
CC Standard and
Content
Mathematical Practices Prior Learning
and Essential Questions
Unit 4.1 (7.1): nth
Roots and Rational
Exponents
N-RN 1, 2
Unit 4.2 (7.2):
Properties of
Rational Exponents
N-RN 1, 2
SMP: 2, 5
What is an nth root?
Using properties
of exponents
SMP: 2, 5, 7
How do you evaluate
expressions with
rational exponents?
Using properties
of exponents
Unit 4.3 (7.3):
Power Functions
and Function
Operations
F-IF 5
F-BF 1
Unit 4.4 (7.4):
Inverse Functions
F-BF 4
SMP: 2, 7, 8
SMP: 2, 5, 7
How do you find the
inverse of a function?
Understand what
a relation is
Unit 4.5 (7.5):
Graphing Square
Root and Cube
Root Functions
A-REI 11
F-IF 4
F-IF 7 b
F-BF 3
SMP:3, 6, 7
What does the graph of
a square root look like?
What does the graph of
a cube root look like?
Graphing basic
functions and
relations
Unit 4.6 (7.6):
Solving Radical
Equations
A-REI 2
SMP: 1, 5
How do you solve
radical equations?
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)
(IA): Review rational exponents and what it means
(IA): Find nth roots without a calculator
(IA): Solve equations using nth roots
(IA): pg. 404 #13-40
(IA): Review properties of exponents and apply
them to rational exponents
(IA): Simplify expressions involving rational
exponents
(IA): pg. 411 #22-81
(FA): Quiz: 7.1-7.2
(IA): Review basic operations on functions
(IA): Introduce the composition of a function
(IA): Find the domain of a composition
(IA): Use composition to solve real world problems
(IA): pg. 418 #12-51
(IA): Find an inverse of a relation and relate that to
the graph
(IA): Find the inverse of a linear and nonlinear
functions
(IA): pg. 426 #16-24, 36-47
(FA): Quiz 7.3-7.4
(IA): Show the parent graph of square roots and
explain how to graph a square root by hand
(IA): Introduce the effects of h and k
(transformations) on a square root graph
(IA): Find the domain and range of a square root
graph
(IA): Show the parent graph of cube roots and
explain how to graph cube root by hand
(IA): Introduce the effects of h and k
(transformations) on a cube root graph
(IA): pg. 434 #15-39
(IA): Demonstrate how to solve radical equations
through various examples
(IA): Individual or group practice solving radical
equations
(IA): pg. 441 #23-54
(SA): Ch. 7 Test
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
Third Quarter
Conceptual Category
Functions
Unit 5 Exponential and Logarithmic Functions (Ch.8)
CC Standard and
Content
Mathematical Practices Prior Learning
and Essential Questions
Unit 5.1 (8.1-8.2):
Exponential
Growth and Decay
A-SSE 1
A-REI 11
F-BF 3
F-IF 7e
SMP: 1, 2, 4, 5, 6,
What do exponential
growth and decay
graphs look like?
What is an asymptote?
Unit 5.2 (8.3): the
number e
A-SSE 11
F-IF 7e
SMP: 1, 4, 5
What is the number e,
and why do we have it?
Unit 5.3 (8.4):
Logarithmic
Functions
A-REI 11
F-IF 4
F-IF 7e
F-BF 4
SMP: 2, 5, 7
What is a logarithm?
Unit 5.4 (8.5):
Properties of
Logarithms
SMP: 2, 5, 7
How do you evaluate a
logarithm?
Unit 5.5 (8.6):
Solving Exponential
and Logarithmic
Equations
SMP: 1, 2, 5
How do you solve an
exponential and
logarithmic equation?
15 days
Graphing basic
functions and
relations
Understand and
use exponents
Solving equations
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)
(IA): Graph basic growth and decay functions
(IA): Describe and demonstrate how to determine if
graph is growth, decay, or neither.
(IA): Introduce the effects of h and k
(transformations) on an exponential graph
(IA): Use exponential growth and decay models to
solve real world problems (including but not limited
to compound interest)
(IA): Create exponential growth and decay
equations to model real world problem and solve
(IA) pg. 469 #13-54, 56-64
(IA) pg. 477 #11-55
(FA): Quiz: Graphing Exponential Functions
(IA or FA): Crash Course in Financial Math
(IA): Simplify natural base expressions
(IA): Describe and demonstrate how to determine if
natural base graph is growth, decay, or neither.
(IA): Use natural base equations to solve real world
problems
(IA): pg. 483 #17-60, 76 -80
(IA): Introduce the definition of logarithm and use
the definition to rewrite expressions between
logarithmic form and exponential form
(IA): Evaluate logarithms without using a calculator
(IA): Find the inverse of a logarithmic function
(IA): Graph a basic logarithmic function
(IA): Introduce the effects of h and k
(transformations) on a logarithmic graph
(IA): pg. 490 #16-70
(IA): Introduce the properties of logarithms and use
to expand and condense logarithmic expressions
(IA): Introduce the change-of-base formula and use
to evaluate a logarithm
(IA): pg. 496 #14-73
(FA): Quiz 8.3-8.5
(IA): Introduce the two ways to solve an
exponential equation
(IA): Introduce the two ways to solve a logarithmic
equation
F-LE 4
(IA): Individual or group practice: solving
exponential and logarithmic equations
(IA): pg. 505 # 25-60
(SA): Ch. 8 Test
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
Third Quarter
Conceptual Category
Algebra
Unit 6
Rational Equations and Functions (Ch. 9) 11 days
CC Standard and
Content
Mathematical Practices Prior Learning
and Essential Questions
Unit 6.1 (9.2+9.3):
Graphing Simple
Rational Functions
A-REI 11
F-IF 4
F-IF 7
SMP: 5, 6, 7
How do you find the
vertical and horizontal
asymptotes?
Graphing
functions and
equations.
Unit 6.2(9.4):
Multiplying and
Dividing Rational
Expressions
A-APR 7
SMP: 2, 7
Are rational functions
closed under
multiplication and
division?
Multiplying and
dividing
polynomials
Unit 6.3 (9.5):
Addition,
Subtraction, and
Complex Fractions
A-APR 6
A-APR 7
Unit 6.4 (9.6):
Solving Rational
Equations
A-REI 2
SMP: 2, 7
Are rational functions
closed under addition
and subtraction?
What is a complex
fraction?
SMP: 1, 2, 5, 7
How do you solve a
rational equation?
Adding and
subtracting
fractions.
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)
(IA): Define rational function and show basic
rational function graph called a hyperbola
(IA): Identify vertical and horizontal asymptotes of
basic and more complex rational functions
(IA): Practice graphing basic rational functions by
hand
(IA): Use a graphing calculator or application to
graph more complex rational functions
(IA): pg. 543 #11-40
(IA): pg. 550 #11-37
(FA): Quiz: Graphing Rational Functions (9.2-9.3)
(IA): Review factoring polynomials
(IA): Review simplifying expressions
(IA): Demonstrate how to multiply and divide
rational expressions by using examples from the
book
(IA): pg. 558 #16-49
(IA): Review adding and subtracting basic fractions
(IA): Demonstrate how to add and subtract rational
expressions by using examples from the book
(IA): pg. 566 #26-46
(FA): Quiz: Multiply, Divide, Add, Subtract Rational
Expressions (9.4-9.5)
(IA): Review least common denominator and how
to find
(IA): Demonstrate how to solve rational equations
by using examples from the book
(IA): Explain how you can get an extraneous
solution
(IA): pg 571 #21-50
(SA): Ch. 9 Test
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
Fourth Quarter
Conceptual Category
Functions
Unit 7
Trigonometric Functions (Ch. 13 and 14)
CC Standard and
Content
Mathematical Practices Prior Learning
and Essential Questions
Unit 7.1 (13.2):
General Angles and
Radian Measure
F-TF 1
F-TF 2
SMP: 2, 5, 7
What is a radian?
What is the unit circle?
Understanding
and using basic
trigonometric
ratios
Unit 7.2 (13.3):
Trigonometric
Functions of any
angle
F-TF1
F-TF 2
SMP: 2, 5, 6
What is a reference
angle?
Understanding
and using basic
trigonometric
ratios
Unit 7.3 (13.4):
Inverse
Trigonometric
Functions
F-TF 7
SMP: 2, 5, 6
What does it mean to
take the inverse of
sine?
Understanding
and using basic
trigonometric
ratios
Unit 7.4 (14.1):
Graphing Sine,
Cosine, and
Tangent Functions
F-IF 7e
F-TF 5
SMP: 2, 4, 5, 7
What does the graph of
sine, cosine, or tangent
look like?
Unit 7.5 (14.2):
Translations and
Reflections of
Trigonometric
Graphs
F-IF 7e
F-TF 5
SMP: 2, 4, 5
Unit 7.6 (14.3):
Verifying
SMP: 2, 3
What is a trigonometric
14 days
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)
(IA): Review angle measures in standard position
(IA): Introduce radian measure and conversions
between radian and degree
(IA): Introduce and complete the unit circle
(IA): Apply arc length to solve a real world problems
(IA): pg. 780 #25-83
(IA): Demonstrate how to evaluate the six
trigonometric ratios at a given point using examples
from the book
(IA): Introduce reference angle
(IA): Use reference angle to evaluate trigonometric
functions
(IA): pg. 788 #23-60
(FA): Quiz 13.2-13.3
(IA): Explain what the inverse of the three basic
trigonometric functions are and apply to all six
trigonometric functions
(IA): Find the angle measure of any trigonometric
ratio
(IA): pg. 795 #18-25, 44-51
(IA): Explain the characteristics of sine and cosine
graphs (range, amplitude, period, frequency) and
how to find these from the equation
(IA): Graph sine and cosine functions
(IA): Use a sine or cosine function to model a real
world problem
(IA): Explain the characteristics of a tangent graph
(IA): Graph tangent function
(IA):pg. 835 #17-49
(IA): Introduce the effects of h and k
(transformations) on a trigonometric function
(IA): Graph a trigonometric function with a vertical
and/or horizontal shift
(IA): Use a sine or cosine function to model a real
world problem
(IA): pg. 844 #17-43
(FA): Quiz: Graphing Trigonometric Functions
(IA): Explain the fundamental trigonometric
identities (may prove some)
Trigonometric
Identities
F-TF 8
identity and how can
you use the identities
to evaluate
trigonometric ratios
(IA): Demonstrate how to find trigonometric ratios
using a trigonometric identity by using examples
from the book
(IA): pg. 852 #16-27
(SA): Trigonometric Test (Ch. 13+14)
Common Core (CC) Standards Curriculum Map Algebra 2
Dan Hayden
Fourth Quarter
Conceptual Category
Statistics and Probability
Unit 8 Statistics and Probability (Ch. 12) <Estimated time in days for completion>
CC Standard and
Content
TBD
Mathematical Practices Prior Learning
and Essential Questions
Instructional Activities(IA)
Formative Assessments(FA)
Summative Assessments(SA)